How many atoms of carbon are present in a diamond weighing 0.5 carat? (one carat weighs 200 mg and assume the diamond to be pure carbon)

Question

How many atoms of carbon are present in a diamond weighing 0.5 carat? (one carat weighs 200 mg and assume the diamond to be pure carbon) (A) 5 × 1021 (B) 6 × 1022 (C) 7 × 1019 (D) 8 × 1012

Tardigrade Admin · Accepted Answer

carat =200 mg 0.5 carat =100 mg 1 mole of C -atoms weight =12 g ⇒ 12 g of carbon =6.023 × 1023 C -atoms ⇒ 100 g of carbon =(6.023 × 1023 × 100/12 × 1000) =5.02 × 1021

Q. How many atoms of carbon are present in a diamond weighing $0.5$ carat? (one carat weighs $200 m g$ and assume the diamond to be pure carbon)

$5 \times 1 0^{21}$

$6 \times 1 0^{22}$

$7 \times 1 0^{19}$

$8 \times 1 0^{12}$

carat $= 200 m g$

$0.5$ carat $= 100 m g$

1 mole of $C$ -atoms weight $= 12 g$

$\Rightarrow 12 g$ of carbon $= 6.023 \times 1 0^{23} C$ -atoms

$\Rightarrow 100 g$ of carbon

$= \frac{6.023 \times 1 0 ^{23} \times 100}{12 \times 1000}$

$= 5.02 \times 1 0^{21}$

Q. How many atoms of carbon are present in a diamond weighing 0.5 carat? (one carat weighs 200mg and assume the diamond to be pure carbon)

5×1021

6×1022

7×1019

8×1012